Orthogonal intertwiners for infinite particle systems in the continuum

Wagner, Stefan

doi:10.1016/j.spa.2023.104269

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2024

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“…The first Hilbert space may be chosen as an extended Fock space, the second Hilbert space is still an L 2 space with respect to a Pascal law with infinite mass α(E) = ∞, and the unitary operator is the isomorphism from chaos decompositions for the Pascal point process [29,Corollary 5.3]. Such an intertwining relation is proven for sticky Brownian motions in [44,Theorem 3.5].…”

Section: Introductionmentioning

confidence: 99%

Intertwinings for Continuum Particle Systems: an Algebraic Approach

Floreani,

Jansen,

Wagner

2024

SIGMA

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We develop the algebraic approach to duality, more precisely to intertwinings, within the context of particle systems in general spaces, focusing on the $\mathfrak{su}(1,1)$ current algebra. We introduce raising, lowering, and neutral operators indexed by test functions and we use them to construct unitary operators, which act as self-intertwiners for some Markov processes having the Pascal process's law as a reversible measure. We show that such unitaries relate to generalized Meixner polynomials. Our primary results are continuum counterparts of results in the discrete setting obtained by Carinci, Franceschini, Giardinà, Groenevelt, and Redig (2019).

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Section: Introductionmentioning

confidence: 99%